One of the root issues surrounding the shutdown (and the upcoming debt ceiling, only nine days away), one of the things that end up getting blamed when people dig down beneath the things argued about on the surface, really isn't too far below the surface at all. Namely, gerrymandering: much of the Republican delegation in the House has been drawn into districts so safe for their party that the only thing they need to worry about is a primary challenge from the right, and with those worries being very real, it behooves them to run as far to the right as possible with no concern for how much the rest of the country despises them.
Now, we've talked about gerrymandering before here, earlier this year, but back in January the topic of concern was a call to delve into the limits of gerrymandering and how far you can draw a district in your favor before the map stops being able to help you. Evidently, we're about to find out in real time what the answer is to that. (That was for academic purposes, people. I didn't want real-world experiments.) The reason I focused on that was because I figured too much time was being spent on basing districts on, often, ultimately unrealistic mathematical constructs focusing on perfectly compact districts. But now I figure I should offer up a suggestion of my own that I reason might be more realistic.
Why do I figure it to be realistic? Because we've already done it. Or at least a version of it.
In the early days of American history, several states allotted multiple seats in the House used a system called general-ticket to fill them. States, in effect, made all of their House seats at-large seats, voted on by the entire state. There were two alternate ways of doing that: either by making each race its own entity, same as now; or by throwing all the candidates into a jungle format and permitting voters to select as many candidates as there were seats, with the top-ranked candidates being seated. This system was phased out with the exception of newly-admitted states, who would use it until they were first able to draw districts.
I say bring it back. The major problem here is that districts are drawn wonky to achieve unrepresentative results. So just get rid of the districts. Everyone that wants to run runs in the same race, and can pick out their own constituency. Take the top votegetters until you fill up the seats.
In fact, this is less feasible due to scale, but ideally I'd look for the entire House to be one big general-ticket election. State lines, in a sense, serve as accidental gerrymandering, splitting like-minded communities across state lines. What would happen here is that the entire United States would become one gigantic district. Go court anyone in America who you feel you represent. On Election Day, you might have little booklets- perhaps reusable to cut down on costs- listing off all the oodles of candidates and, as a way of differentiating between the inevitable similarly-named candidates, hometowns as well. A voter would go into the booth and vote for... I'll give them up to five candidates. The top 435 candidates get seated.
You would definitely see at least a couple third-party candidates scrabble together enough votes to ensure one or two seats (not a full-fledged multiparty setup, though; the Senate and Presidential elections remain unchanged). You would also see some unshakable fringe factions such as the Tea Party. The thing is, though, that fringe is all they would get to be. The issue of the Tea Party driving other members right for fear of a primary, I don't think, would come up. They could try, but it would fail, because the race wouldn't work that way. The House that resulted would gravitate away from the two-party format of first-past-the-post and more towards a coalition-building model common in parliamentary systems. The (hopefully) saner whole could build a coalition without the fringe. You cede a few seats to save the whole.
And I don't think the ideological makeup would be the only factor. Perhaps it doesn't take all that much to cross the goal line and become the last person who makes the cut. Congratulations! You've made it into Congress! But you came in 435th and everybody knows it. Everybody knows you have zero margin for error with the voters and are extremely susceptible to being voted out. There isn't much point in giving you very much power or influence. Not until you make yourself a little safer by climbing up the ladder next election. The real influence would more likely go to the people who finish in the top couple dozen, those who gained the most approval from the voters. Those on the bubble would be more likely to be relegated to the backbench, headcount at voting time and little more.
No matter what voting system you use, those fringes will still be there. That can't be fixed by this or any other system. After all, this is supposed to be reflective of the will of the people, and if the people vote for idiots, idiots are what we shall have.